【摘要】 考虑地表水的渗透和扩散作用对干旱半干旱地区生态系统的影响,本文建立了具有时变时滞的反应扩散植被-水系统模型.给出阈值R~*,并讨论了系统的动力学行为,当R~*<1时,系统的无植被平衡点局部渐近稳定.当R~*> 1,植被一致持久.此外,通过拉丁方抽样(LHS)及偏秩相关系数(PRCCs)方法对模型阈值进行敏感性分析,给出了参数对系统动力学行为的影响并为制定防治荒漠化的措施提出建议.此外,通过分析系统有限时间稳定性,讨论了时滞对植被水模型的动力学行为的影响.更多还原

【Abstract】 Considering the effects of infiltration and diffusion of surface water on the ecosystems in arid and semi-arid areas, a reaction-diffusion vegetation-water system with time-varying delay is established in this paper. A threshold value R~* is defined, and the dynamic behaviors of the system related to the threshold value are discussed. When R~*> 1, the vegetation-free equilibrium point of the system is locally asymptotically stable. When R~*< 1, the vegetation is uniformly persistent. In addition, the sensitivity analysis of the threshold is carried out by Latin Hypercube Sampling(LHS) and partial rank correlation coefficients(PRCCs) methods, the influence of parameters on the dynamic behaviors of the system is discussed, and some suggestions for measures to prevent desertification are given. In addition,the influence of time delay on the dynamic behaviors of the vegetation-water system are discussed, by analyzing the finite-time stability of the system.更多还原